Recall that \(\mathsf {RCD}(K,\infty )\)  spaces are (possibly non-smooth) metric measure spaces having Ricci curvature bounded below by \(K\in \mathbb {R}\)  and no upper bound on the dimension, in a synthetic sense. More precisely, \(\mathsf {RCD}(K,\infty )\)  spaces are the sub-class of \(\mathsf {CD}(K,\infty )\)  spaces introduced in the seminal works of Sturm [1]} and Lott-Villani [2]} having the canonical energy functional (called “Cheeger energy") satisfying the parallelogram identity. The reader is referred to Section  for the precise definitions, and to [3]} for a survey.
The class of \(\mathsf {RCD}(K,\infty )\)  spaces was singled out by Ambrosio-Gigli-Savaré [4]} (see also [5]}) who developed a powerful calculus in this setting.
